I was wondering if someone can give me a general definition of a min-cut besides it being the max flow of a network.
For example, in the baseball elimination problem, if we wanted to find out if team z is eliminated, the min cut represents the team(s) that will beat team z out of the 1st place if the edges aren't full saturated. If the edges are fully saturated, then min-cut is everything except t, and team z still has a chance.
For the project selection, the min cut contains the projects you should do to maximize your return.
How do people figure out that min-cut can be applied to these problems? What is it about min-cut that gives it such power?